Problem: Solve for $x$ and $y$ using substitution. ${-3x+5y = -2}$ ${x = 4y-11}$
Since $x$ has already been solved for, substitute $4y-11$ for $x$ in the first equation. ${-3}{(4y-11)}{+ 5y = -2}$ Simplify and solve for $y$ $-12y+33 + 5y = -2$ $-7y+33 = -2$ $-7y+33{-33} = -2{-33}$ $-7y = -35$ $\dfrac{-7y}{{-7}} = \dfrac{-35}{{-7}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {x = 4y-11}\thinspace$ to find $x$ ${x = 4}{(5)}{ - 11}$ $x = 20 - 11$ ${x = 9}$ You can also plug ${y = 5}$ into $\thinspace {-3x+5y = -2}\thinspace$ and get the same answer for $x$ : ${-3x + 5}{(5)}{= -2}$ ${x = 9}$